Over the centuries, for as long as information has been communicated between two individuals, it has been susceptible to third-party interception, eavesdropping, compromise and/or corruption. Traditionally, this problem has been handled through the development, over the years, of increasingly sophisticated cryptographic techniques.
Key-Based Ciphers
One class of these sophisticated cryptographic techniques involves the use of key-based ciphers. In particular, through a key-based cipher, a sequence of intelligible data (i.e., plaintext) that collectively form a message are mathematically transformed, through an enciphering algorithm, into seemingly unintelligible data (i.e., so-called ciphertext).
As a practical matter, a particular cipher that generates any given ciphertext should be sufficiently secure from cryptanalysis. To provide a requisite level of security, a unique key is typically selected which defines a unique corresponding cipher.
Generally speaking, the strength of any cryptographic technique (and hence the degree of protection it affords from third-party intrusion) is directly proportional to the time required, by a third party, to perform cryptanalysis. With a key-based cipher, cryptanalysis is where a third party is able to successfully convert the ciphertext into its corresponding plaintext without prior knowledge of the key.
As technology evolves, the art of cryptography advances in a continual effort to develop increasingly sophisticated cryptographic techniques that withstand correspondingly intensifying cryptanalysis.
Short Signatures
Digital signatures on binary messages are the digital equivalent of human signatures on printed documents. Signatures must be short in environments with strong bandwidth constraints. For example, software product registration systems often ask users to enter a signature provided on a product label.
Primarily for customer service reasons and other practical constraints, it is highly desirable to use a short signature when a human is asked to manually enter the signature. Similarly, due to space constraints, short signatures are desirable when one prints a bar-coded digital signature on a postage stamp. Also, legacy protocols typically have a fixed short field for non-repudiation.
However, the shorter a signature is, the easier that it is for a digital pirate to break the system by cryptanalysis. Therefore, schemes have been developed with the intent of increasing the security of a cipher given an allotted fixed field length.